Tumbling and polishing machines are known in the art. In German Patent 1,652,065, for example, the carrousel disks are flat plates; the drums are arranged parallel to one another and are rotated about the axis of the carrousel disks in a stationary frame with a fixed angle of inclination to the vertical or to the horizontal. This fixed angle of inclination of the drums leads in many cases to unsatisfactory results in the known machine, the frame supporting the carrousel disks is suspended in a fixed stand and swivel-mounted about an axis running vertically to the axis of rotation of the carrousel disks, there being a gimbal suspension of the carrousel disks as a whole. Thus, by a swivel movement of the frame, the drums can be set into a tumbling motion during their rotation. Although this type of suspension facilitates the emptying of the drums, it is very complicated and susceptible to breakdown, particularly since, during operation, the rotating carrousel is never completely balanced. Additionally, the drive of the entire apparatus poses difficult problems. Either the drive of the carrousel must be carried out on gimbals, which leads to irregularities in the course of motion when the frame carrying the carrousel is swivelled, or the driving motor for the carrousel must be mounted in a swivel frame and moved together with the carrousel. The motor for the drums must, of necessity, be positioned in one of the carrousel disks, so that the motor as well must be moved in the swivel motion. The mass to be swivelled is thus relatively great and must be supported by all the bearings. The tumbling motion, which is necessary in order to attain a good polishing effect, makes it moreover impossible to fill or empty the drums while in operation.